Download A Bandpass filter-bank model of auditory sensitivity

Aquatic Mammals 2001, 27.2, 82–91
A Bandpass filter-bank model of auditory sensitivity in the
humpback whale
Dorian S. Houser1, David A. Helweg2* and Patrick W. B. Moore3
1
National Research Council Associate, SPAWARSYSCEN-San Diego, San Diego, CA 92152, USA
2
Code 3501E, SPAWARSYSCEN-San Diego, San Diego, CA 92152, USA
3
Code 3501B, SPAWARSYSCEN-San Diego, San Diego, CA 92152, USA
Abstract
Concerns that water-borne, anthropogenic sound
could negatively impact whale species continue to
escalate. Unfortunately, the auditory sensitivity of
mysticete whales is unknown, impeding assessment
of underwater sound exposure on these animals. In
light of this problem, a mathematical function
describing frequency sensitivity by position along
the relative length of the basilar membrane of a
humpback whale (Megaptera novaeangliae) was integrated with known data on the cat and human to
predict the audiogram for the humpback whale.
The predicted audiogram was the typical mammalian U-shape and indicated sensitivity to frequencies from 700 Hz–10 kHz, with maximum
relative sensitivity (values approaching 0) between
2–6 kHz. A model of humpback hearing subsequently was created as a series of pseudo-Gaussian
bandpass filters. Sensitivity of the model was optimized to the predicted audiogram via metaevolutionary programming (EP). The number,
frequency distribution, and shape of the filters in
the model were evolved with the EP and the sensitivity of the model evaluated through a simulated
hearing test. Maximum deviations between model
sensitivity and predicted humpback sensitivity
never exceeded ten percent. Through an integrated
approach, the first predicted humpback audiogram
was made and used to develop the first bandpass
model of the humpback ear.
Key words: audiogram, evolutionary program,
filter model, hearing, humpback whale, anthropogenic sound
Introduction
A substantial increase in anthropogenic noise in the
marine environment has occurred over the last
century as a result of increased scientific exploration, shipping traffic, geophysical and oil industry
? 2001 EAAM
activities, and military operations. For many
marine species that are sensitive to acoustic signals
or reliant on them for communication, foraging,
reproduction, or navigation, the impact of exposure
to such sounds is unknown. Anthropogenic noise
can potentially interfere with the production or
reception of these signals through masking,
behavioral disturbances, temporary threshold
shifts, or permanent damage to the auditory system
(Richardson & Würsig, 1997). Of primary concern
are mysticete whales (baleen whales) whose sounds
range from 15 Hz–8000 Hz, suggesting auditory
sensitivity to frequencies commonly generated by
anthropogenic sources (Clark, 1990; Herman &
Tavolga, 1980; Richardson & Würsig, 1997).
Assessment of such impacts to date has been limited
to observations of mysticete responses to industrial
sound exposure and playbacks of anthropogenic
signals (Frankel & Clark, 1998; Malme et al., 1985;
Malme et al., 1988; Maybaum, 1989; Richardson
et al., 1990; Richardson et al., 1985). Unfortunately, interpretation of experimental results has
been confounded by the intra- and inter-specific
variability in observed behavior and, in some
instances, an apparent lack of correlation between
whale behavior and received sound level.
Mysticetes are too large to maintain in a controlled environment necessary for effective traditional audiometric assessment. Psychophysical
and physiological studies of cetacean (baleen and
toothed whales) hearing have been restricted to
the smaller odontocetes (toothed whales), with the
bottlenose dolphin (Tursiops truncatus) being the
species studied most (Au, 1993; Au & Moore, 1990;
Busnel & Fish, 1979; Herman & Arbeit, 1972;
Johnson, 1968a, 1968b; Nachtigall & Moore, 1988;
Popov et al., 1996; Popov et al., 1997; Supin et al.,
1993). Using psychophysical measures of dolphin
hearing and the anatomy of the dolphin auditory
system, Roitblat and colleagues (1993) constructed
a model of the dolphin ear as a series of overlapping
frequency-domain filters. Sensitivity to acoustic
Auditory sensitivity in the humpback whale
83
signals above 50 kHz was comparable to that
observed in the dolphin and was later improved
across the full range of dolphin hearing through the
application of evolutionary programming (EP)
(Houser et al., 2001), an optimization technique that emulates natural evolutionary processes.
Extending these types of models to mysticete audition is a logical step towards predicting mysticete
sensitivity to anthropogenic sounds, particularly
since more direct psychophysical and physiological
procedures are not likely in the immediate future.
It can be argued that mysticetes have a conventional mammalian ear adapted to low frequency
reception due to the presence of a voluminous
middle ear cavity and the loose coupling of the
ossicles (Ketten, 1997). Furthermore, the anatomy
and biomechanical properties of the basilar membrane can be used to predict frequencies to which
terrestrial mammals are sensitive (Greenwood,
1990), and this approach has been extended and
modified to predict frequencies to which whales are
sensitive (Ketten, 1994; Ketten & Wartzok, 1990;
Norris, 1981). If it is assumed that mysticetes have
a conventional mammalian ear, and a cochlear
frequency-position function can be determined
from the cochlear anatomy, then psychoacoustic
and anatomical measures of hearing from a terrestrial mammal with a conventional ear can be used
to create a predictive mysticete auditory threshold
function. A bandpass ear-filter model can then be
constructed and output optimized to the predicted
threshold as has been performed for the bottlenose
dolphin (Houser et al., 2001; Roitblat et al., 1993).
The objective of this study was to create a
mathematical model of a mysticete ear, specifically
that of the humpback whale (Megaptera novaeangliae). Anatomical indices of hearing were derived
for the humpback from histological measurements
of the basilar membrane and related structures
(Ketten, in preparation), thus providing the
cochlear frequency-position function necessary for
model development. In the first part of the study,
we generated a predicted audiogram for the humpback whale. In the second part of the study, evolutionary programming techniques were used to
create a bandpass-filter model with output that
matched the predicted humpback whale audiogram.
frequency-position function of two well-studied
terrestrial mammals, the cat and human, and
mapping the resulting sensitivity-position functions
onto the frequency-position map of the humpback
whale ear.
A basilar membrane frequency-position function
was determined from morphometric analyses of
extracted humpback whale basilar membranes. The
method for determining the frequency response of
the basilar membrane by position along its length is
the subject of an upcoming paper and the methodological details are not presented here (Ketten, in
preparation; but see Ketten, 1993, and Ketten,
1994, for summaries of previous modeling effort).
Ten estimates of frequency by position along the
basilar membrane were supplied from these analyses (D. Ketten, personal communication) and the
distribution of frequencies along the relative length
of the basilar membrane fit with a 3rd order exponential function (Figure 1, r2 =0.99). The exponential function, thus became the frequency-position
function for the humpback basilar membrane.
Auditory thresholds and cochlear frequencyposition functions of the cat and human were
integrated with the humpback frequency-position
function to create an audiogram for the humpback
whale. The goal of this procedure was to generate
an audiometric function generally in agreement
with other observed mammalian thresholds. Scaled
threshold values were combined so that any auditory specialization would be averaged out to some
degree. This procedure does not imply that either
the cat or human audiogram is more similar to the
audiogram of the humpback whale than are other
mammalian species. They are simply two species
with conventional mammalian ears. Other species
with generalist audiograms could have been
utilized.
Cochlear frequency-position functions were
obtained for the human (Greenwood, 1990) and cat
(Liberman, 1982) and adjusted such that exponential coefficients accommodated the expression of
basilar membrane length in proportional units.
Thus, for the human:
Materials and Methods
f(x)=456(102.1x "0.8)
Predicting the humpback whale audiogram
Since empirical auditory threshold measurements
for the humpback do not exist, an audiometric
function predicting the frequency-dependent relative sensitivity was created on the assumption
that the humpback ear could be modeled as a
conventional mammalian ear. This task involved
integrating the auditory threshold function and
f(x)=165.4(102.1x "1)
(1)
and for the cat:
(2)
where, f(x) is frequency and x is a proportion of
basilar membrane length. For all frequencies at
which hearing thresholds have been tested in the
human and cat, as reported by Fay (1988), the
respective relative position on the basilar membrane
was determined. Relative position determinations
for the cat were limited to frequencies between
D. S. Houser et al.
Frequency (kHz)
84
15
10
5
0
0
20
40
60
80
Basilar Membrane Length (%)
100
Figure 1. Frequency plotted against relative position on the basilar membrane for the humpback
whale (data provided by D. Ketten). A 3rd order exponential function was fit to the data
(y=0.08*exp(0.15x"(8.74e-4)x2 +(1.63e-6)x3)) to create the frequency-position function.
100 Hz and 60 kHz since this was the frequency
range covered by the experimentally determined
basilar membrane frequency-position function
(Liberman, 1982). Frequencies from 64 Hz–
18,780 Hz, reported in Fay (1988) for adult human
auditory thresholds, fell within the experimentally
determined frequency-position function of the
human basilar membrane (Greenwood, 1990).
Frequency-dependent threshold intensities (W/
cm2) of the cat and human were plotted as a
function of relative basilar membrane position.
Threshold intensities were converted to dB re:
minimum intensity and fit with a 4th order polynomial (Figure 2, r2 =0.66). This intensity-position
function was integrated with the humpback cochlear frequency-position function to produce an
audiogram for the humpback. Thresholds were
subsequently scaled from zero to one.
Optimized filter-bank ear model design
Development of a computational ear model, similar
to that described by Houser and colleagues (2001)
for the dolphin, relies on the existence of a target
threshold function to which sensitivity can be optimized. To create a computational ear model, the
predicted humpback whale audiogram (Figure 3)
was used as the target threshold function. Relative
threshold values for frequencies used in ear model
development, that were not explicitly defined by the
humpback audiogram, were determined via cubic
spline interpolation.
Ear models were created as a series of overlapping bandpass filters with a pseudo-Gaussian (PG)
shape, as described for the bottlenose dolphin
(Houser et al., 2001). Filter shapes were ’pseudoGaussian’ in that the standard deviation (ó) was
removed from the denominator of the distribution
equation to control variations in filter amplitude
that accompany changes in ó. These were not
digital IIR or FIR filters; instead, the Gaussian
shape delimited the bandpass region in the spectral
power domain. Pseudo-Gaussian filter shapes
were generated with peak sensitivity corresponding
to the center frequency (ì) of the filter, according
to:
where, xi is the ith point on the distribution curve.
Each filter was described by a 256 bin vector with
each bin corresponding to a 100 Hz width such that
the frequency range covered by the filter shape was
20.1–25.6 kHz.
Filter center frequencies were distributed from
100 Hz to 18 kHz. Restriction of filter center frequency to a maximum of 18 kHz was performed to
minimize sensitivity above 18 kHz, a characteristic
Auditory sensitivity in the humpback whale
85
50
dB re: MIN Intensity
Cat
Human
40
30
20
10
0
0.0
0.2
0.4
0.6
0.8
1.0
Relative Basilar Membrane Position
Figure 2. Relative hearing sensitivity of the cat and human as a function of relative basilar
membrane length. The relationship was determined by integrating experimentally derived
frequency-position functions (Greenwood, 1990; Liberman, 1982) for each species with their
respective averaged frequency-dependent thresholds (obtained from Fay, 1988). The fitted function
(y=3.36"12.4*x+19.72*x2 "19.1*x3 +11.75*x4) provides a predictive sensitivity-position
function.
of the predicted humpback audiogram. Filter center
frequency (ì) was calculated as a fractional power
of the frequency range emulating the non-uniform
spacing of characteristic frequencies on the basilar
membrane (Geisler & Cai, 1996). The equation
was:
where, Fn is defined as the total number of filters
used in the model, fj was the jth filter, and the
constant 180 was used to describe the predicted
range of hearing (i.e., 180#100 Hz binwidth=
18 kHz).
Variation in filter shape was achieved by implementing a frequency-dependent amplitude-scaling
factor (S) and 3-dB bandwidth (Q3) function for
each filter. Q3 was determined as an exponential
function of filter center frequency so that bandwidth ranged from constant-Q to a curvilinear
variation with center frequency. It was defined as
the ratio of ì to the bandwidth at 3 dB below the
peak amplitude of the filter in the spectral power
domain. The relationship between ó and Q3 was
derived from the PG equation as:
where, á=2.351. The value of á was empirically
determined in the power domain by systematically
varying ì and Q3 and observing the relationship to
ó. Amplitude scaling was determined using a
frequency-dependent function that could create a
bank of filters, ranging from equal gain to a bank of
filters with variable gain. The scaling factor, S, was
determined as a base value to a negative fractional
power derived from sequential filter position within
the frequency range such that:
where, y is an evolved base value. This factor is
analogous to the scaling used by Roitblat et al.
(1993), which was based upon hair cell densities
along the basilar membrane. The scaling factor was
loosely defined in this model implementation
so that the evolutionary program would not be
constrained in its search for a suitable model
structure. Substitution of parameters into the
D. S. Houser et al.
Relative Hearing Sensitivity
86
1.0
0.8
0.6
0.4
0.2
0.0
0.01
0.1
1
10
100
Frequency (kHz)
Figure 3. Relative hearing sensitivity function created by scaling humpback frequency-dependent
sensitivities from 0–1. Prior to scaling, frequency-dependent sensitivities were determined by
integrating the humpback frequency-position function (Figure 1) with the sensitivity-position
function derived from cat and human audiometric and anatomic data (Figure 2).
pseudo-Gaussian equation thus produced the filter
form function:
The filter bank model assumes that, since model
design is optimized to threshold conditions, the
transfer functions of the outer and middle ear are
translated, and therefore reflected, in basilar membrane motion at levels of threshold exposure. This
static condition does not require that middle and
outer ear transfer functions be addressed, they are
implied in the model and reflected in the filter
design. Furthermore, transfer functions for the
middle and outer ear have yet to be defined for
the humpback whale, obviating their inclusion in
the model.
Evolutionary programming (EP)
Parameters determining filter shape and distribution were submitted to an EP scheme with selfadaptive mutation (Fogel, 1995) and a Cauchy
mutation operator (Chellapilla & Fogel, 1997).
Through an iterative process of parameter cloning,
parameter mutation, and model evaluation the EP
optimized the sensitivity of populations of encoded
ear models to that of the predicted humpback
audiogram. The EP used 20 ’parent’ parameter sets
with 20 ’offspring’ produced per generation, a form
of evolutionary algorithm (EA) commonly known
as a (20+20)"EA (Schwefel, 1981). The reader is
referred to Houser et al. (2001) for a thorough
description of the EP process and its application to
biomimetic filter design.
Parameters of the evolutionary program are
given in Table 1, which lists respective random
initialization boundaries and the initial standard
deviation used in calculating mutation step-size.
Parameters including the base value (y) of the
amplitude scaling factor (S) and the equation determining Q3 were mutated via a Cauchy random
variable (Chellapilla & Fogel, 1997). The total
number of filters (Fn) was mutated in a probabilistic
manner such that there was an equal probability
that Fn would increase by 1 or 2, decrease by 1 or 2,
or stay the same, if 20<Fn <400. If Fn¦20, there
was an equal probability that Fn would increment
by 1, 2, or stay the same. Conversely, if Fn§400,
there was an equal probability that Fn would
decrement by 1, 2, or remain the same. Thus,
minimum and maximum possible values of Fn were
19 and 401, respectively.
Following each generation of the evolutionary
program, defined by parameter cloning and mutation, sets of parameter values were inserted into the
filter function described in Equation 7 to create a
bank of filters. Each filter bank was evaluated for
its sensitivity through a simulated audiometric assessment at {0.1, 0.2, 0.3, . . ., 0.9} and {1.0, 2.0,
3.0, . . ., 19.0} kHz, for a total of 28 comparison
frequencies. This was achieved by first creating a
library of noise (N) and signal+noise (S+N) trials
Auditory sensitivity in the humpback whale
87
Table 1. Model parameter values with initialization limits, initial standard deviations, and
description of parameter function.
Parameter
y
m
b
x
Fn
Minimum
initialization limit
Maximum
initialization limit
Initial
standard deviation
0
0
0
0
(b)
10
10
2
0.025
(b)
0.5
0.5
0.15
0.001
(c)
Definition (a)
y
m
b
x
Fn
base value for filter amplitude scaling (used to calculate S
slope of the equation determining Q3
intercept of the equation determining Q3
coefficient of the exponent in the equation determining Q3
filter number
(a) See Houser et al. (2001) for details on the equations determining S and Q3.
(b) Filter number explicitly set to 40.
(c) Probabilistic mutation limited to integer step sizes of &2.
with which to test the sensitivity of the filters. Each
library consisted of a 5000#256 matrix with row
elements corresponding to a binwidth of 2100 Hz,
i.e. equivalent to the frequency distribution
described for the filter arrays. To simulate noise,
bins were initialized with randomly generated
values ranging from 0.00 to 0.25. In the S+N
library, a real valued ’signal’ of 0.55 was added to
the bin corresponding to a given frequency. For
instance, to add a signal to the 1 kHz frequency of
the S+N library, 0.55 was added to the value of the
10th bin of each row of the library. This matrix thus
became the 1 kHz S+N library, or (S1 +N).
The response of the filters to N trials (RN) and
Sf +N trials (RSNf) was derived by multiplying the
filter matrix by the rows of the N library, and rows
of the Sf +N library, respectively, for a given test
frequency such that:
RN(i)=F*N(i), i=1, 2, 3, . . ., 5000
(8)
RSNf(i)=F*SNf(i), i=1, 2, 3, . . ., 5000
(9)
where, N and SNf represent the row vectors of the
N library and the (Sf +N) library at frequency f. A
squared-difference (SD) vector was then determined
as:
SD(i) =[RSNf(i)"RN(i)]2,
i=1, 2, 3, . . ., 5000 (10)
and the sensitivity metric ( f) for the tested frequency determined as:
where, Fn denotes the number of filters in the
model. The process was repeated for all values of f,
i.e., all 28 test frequencies. This specific procedure
was implemented to emulate the effect of the
traveling wave on the basilar membrane. Output of
individual filters was assumed to be representative
of neural (hair cell) stimulation and the scalar
output representative of the contribution of all
filters at a given frequency. The filter bank response
was then assumed to be proportional to auditory
sensitivity.
All values of f were normalized from 0 to 1 to
form the response curve of the humpback ear
model. This function was compared to the predicted
humpback whale audiogram described in Part 1.
The absolute value of the maximum deviation
between the ear model response curve and the
predicted humpback audiogram across all tested
frequencies was used as the performance metric (Pe)
for tournament selection (Goldberg & Deb, 1991).
Following sensitivity testing of all of the models in
a generation, selection of parameter sets for inclusion in the next generation was determined via
tournament selection with a tournament size of 10
(Goldberg & Deb, 1991).
EPs were run at the Navy High Performance
Computing
Center
(SPAWARSYSCEN-San
Diego) on a Hewlett-Packard V2500 multiprocessor system. The V2500 utilized 16 440-MHz
88
D. S. Houser et al.
4-way superscalar PA-8500 processors and 16 GB
of RAM. Program code was multithreaded according to POSIX standards in order to take advantage
of the HPC parallel processing capabilities (Norton
& Dipasquale, 1997). Three EP simulations were
performed with the predicted humpback sensitivity
curve used as the target function. After each generation of a trial, the minimum Pe value produced
by the current population of parameter sets was
recorded. Trials were terminated if Pe decreased by
less than 0.001 over a series of 100 generations.
Results
Predicting the humpback whale audiogram
The predicted humpback whale audiogram is presented in Figure 3. Sensitivity is plotted on a
relative dB scale since there are no estimates of
absolute auditory sensitivity for the humpback. The
relative auditory sensitivity prediction for the
humpback was U-shaped and typically mammalian.
The region of best hearing, defined as relative
sensitivity ¦0.2, ranged from 700 Hz to 10 kHz, a
range of almost 4 octaves. Maximum sensitivity,
that which approached a value of zero, ranged from
2–6 kHz. Reduction in sensitivity was approximately 16 dB/octave above 10 kHz. Frequency sensitivity between 200–700 Hz was comparable to that
between 10–14 kHz, both ranges covering relative
sensitivities between 0.2 and 0.5, but with a shallower reduction in low frequency sensitivity of
approximately 6 dB/octave. The most insensitive
frequencies occurred at 100 Hz and frequencies
§15 kHz.
Note that the broad range of frequencies to
which humpbacks are predicted to be sensitive
corresponds well to the range of frequencies
reported for humpback whale sounds (Helweg
et al., 1998; Helweg et al., 1990; Payne, 1983).
Sound ranges are expected to reflect the same
range of frequencies to which the whales would be
sensitive.
Ear model performance
All ear filter models performed similarly. The
best performing ear filter model had a Pe =0.09
(Figure 4b), a slightly better performance than
the Pe =0.10 achieved by the other two models
(Figure 4a and 4c). Two of the models converged
upon configurations of 401 filters (Figure 4a and
4b) while the third utilized 263 filters (Figure 4c).
Equations for determining filter Q3 and the base
value (y) of the amplitude scaling factor (S) were,
respectively:
(Figure 4a)
Q3 =0.76*exp((1.4e-2)*ì)+0.34, y=2.92
(Figure 4b)
Q3 =0.69*exp((1.5e-2)*ì)+0.23, y=3.51
(Figure 4c)
Q3 =0.74*exp((1.2e-2)*ì)+0.69, y=2.06
Maximum deviations tended to occur above
5 kHz, though the 263-filter model configuration
produced seven equivalent maximum deviations
across the predicted range of hearing. Nevertheless,
reduction in sensitivity above 10 kHz occurred at a
rate similar to that predicted by the humpback
audiogram. Frequencies of best sensitivity were at 3
and 5 kHz for all models and there was a consistent
sensitivity roll-off below 700 Hz.
Discussion
In this study, a frequency-position function
derived from the morphometry of the humpback
whale basilar membrane (Ketten, in preparation)
was combined with conventional land mammal
psychoacoustic data and anatomical indices of
hearing. As a result, the first audiogram for the
humpback whale was predicted. This model provides a tool with which to aid mitigation of the
acoustic exposure of humpback whales until such
time that actual auditory sensitivities for these
animals can be determined. Similar tools could be
developed for other species of mysticete whale
provided the anatomical data necessary for creating
a frequency-position function are obtainable.
The ear models presented here are frequency
spectrum filters or auditory weighting functions
that allow a prediction of how the humpback
auditory system attenuates sound according to frequency. It can be used to predict the magnitude of a
frequency component of a received complex signal
relative to that of other frequency components after
filtration by the peripheral auditory system. Such
predictions can improve the contextual interpretation of the response of mysticetes to sound
exposure when the level of the signal received by the
whale is known or can be estimated. These models
only make use of frequency domain information
and assume a static, but undefined, contribution of
the outer and middle ear that is reflected in filter
design. The model does not incorporate time
domain characteristics or the dynamic contributions of the middle and outer ear. Advancement
into more realistic lumped parameter models that
account for additional mechanical properties of
the auditory system is the next logical step. Such
models provide a means of including the dynamic
effects of middle and inner ear anatomy on system
function and are more biologically relevant.
Although these types of models have been applied
to terrestrial mammals (Hubbard & Mountain,
Auditory sensitivity in the humpback whale
89
1.0
Predicted
0.8
Evolved
0.6
0.4
Relative Hearing Sensitivity
0.2
0.0
1.0
0.8
0.6
0.4
0.2
0.0
1.0
0.8
0.6
0.4
0.2
0.0
0.01
0.1
1
10
100
Frequency (kHz)
Figure 4. Comparison of the best-performing ear model output,
from each evolutionary programming trial (panels a, b and c), to
the predicted humpback relative sensitivity function. Triangles
correspond to frequencies at which maximum deviations between
the predicted humpback sensitivity function and model output
occurred.
1996; Rosowski, 1996), their utility in modeling the
auditory systems of marine mammals has yet to be
realized.
Humpback whale songs span from near infrasonic frequencies to over 8 kHz (Helweg et al.,
1998; Helweg et al., 1990; Payne, 1983). Predictions
of hearing range reported here are in agreement
with observed sound production for the humpback,
which presumably lies within the range of hearing.
Although the predicted audiogram demonstrates a
plausible frequency-sensitivity shape, the zone of
best sensitivity (22–6 kHz) is somewhat higher
than one would predict after inspecting the distribution of frequencies used in humpback song. This
is most likely explained by the contribution of the
human and cat threshold functions to the predicted
humpback whale audiogram. Although the use of
these values provided a generalized audiometric
function for integration with the humpback whale
basilar membrane frequency-position map, use of
thresholds obtained from other mammals would
undoubtedly cause some variation in the resulting
U-shape. Thus, when implementing the humpback
ear filter models, caution must be exercised when
interpreting the results.
Methods of determining the impact of anthropogenic noise on mysticete whales will continue to rely
heavily on the use of playback experiments and
opportunistic observations of mysticete responses
to the exposure of human-made sound. Models of
mysticete hearing can augment these methods and
should be pursued. The first bandpass filter models
of the humpback whale ear are presented here
to provide a means for contextually improving
90
D. S. Houser et al.
interpretations of behavioral responses to sound
exposure. These models should be used and built
upon as more information about mysticete hearing
becomes available and until such time that absolute
auditory thresholds are experimentally determined.
Acknowledgments
This modeling effort was made possible by the
estimates of humpback whale basilar membrane
resonant frequencies generated by Dr. Darlene
Ketten of the Woods Hole Oceanographic
Institution, under contract from the Strategic
Environmental Research and Development Program Project CS-1082. We thank the Space and
Naval Warfare Systems Center High Performance
Computer Center for their grant of CPU time on
the HP V2500. This study was possible in part
thanks to funds from PMS-400DE and SERDP
Project CS-1082. The procedures involved in this
study comply with the ’Principles of Animal Care’,
publication No. 86-23 (revised 1985), of the
National Institute of Health and with the current
laws of the United States of America.
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